A triatomic molecule can have a linear configuration, as does CO2 (Figure a), or it can be nonlinear, like H2O (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. (a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear? Eint/nT = ? (b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear? Eint/nT = ? At high temperatures, a triatomic molecule has two modes of vibration, and each contributes 0.5R to the molar specific heat for its kinetic energy and another 0.5R for its potential energy. (c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary: R.) Eint/nT = ?
A triatomic molecule can have a linear configuration, as does CO2 (Figure a), or it can be nonlinear, like H2O (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. (a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear? Eint/nT = ? (b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear? Eint/nT = ? At high temperatures, a triatomic molecule has two modes of vibration, and each contributes 0.5R to the molar specific heat for its kinetic energy and another 0.5R for its potential energy. (c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary: R.) Eint/nT = ?
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I'm hoping for a good explanation of how to do this. I'm also wondering why it matters if the configuration is linear or nonlinear?
A triatomic molecule can have a linear configuration, as does CO2 (Figure a), or it can be nonlinear, like H2O (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible.
(a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear?
Eint/nT = ?
(b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear?
Eint/nT = ?
At high temperatures, a triatomic molecule has two modes of vibration, and each contributes 0.5R to the molar specific heat for its kinetic energy and another 0.5R for its potential energy.
(c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary: R.)
Eint/nT = ?
Eint/nT = ?
Transcribed Image Text:### Chemical Bonding: Molecule Structures
#### Diagram a
This diagram illustrates a linear molecular structure. It depicts a carbon dioxide (CO2) molecule, consisting of one carbon (C) atom centrally positioned and double-bonded to two oxygen (O) atoms, placed symmetrically on opposite sides.
#### Diagram b
This diagram represents a bent molecular structure, specifically that of a water (H2O) molecule. It shows one oxygen (O) atom at the center with two hydrogen (H) atoms bonded to it at an angle, forming a characteristic bent shape. The diagram highlights the angular arrangement due to the two pairs of unshared electrons on the oxygen atom, which influence the molecule's shape.
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